Stem pythagorean theorem introduction

7.17.1 Apply the Pythagorean TheoremBell Thinger

2. Solve x2 + 9 = 25.

ANSWER 10, –10

ANSWER 4, –4

1. Solve x2 = 100.

ANSWER 2 5

3. Simplify 20.

ANSWER 6 cm

4. Find x.

Video attached

7.1

7.1

Find the length of the hypotenuse of the right triangle.

Example 1

SOLUTION

(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem

x2 = 62 + 82

x2 = 36 + 64

x2 = 100

x = 10 Find the positive square root.

Substitute.

Multiply.

Add.

7.1Guided Practice

Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.

1.

ANSWER Leg; 4

7.1

Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.

2.

13hypotenuse; 2ANSWER

Guided Practice

7.1Example 2

SOLUTION

= +

7.1

Find positive square root.

Substitute.

Multiply.

Subtract 16 from each side.

Approximate with a calculator.

162 = 42 + x2

256 = 16 + x2

15.492 ≈ x

240 = x2

The ladder is resting against the house at about 15.5 feet above the ground.

ANSWER The correct answer is D.

Example 2

√240 = x

7.1Guided Practice

The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder?

3.

about 23.8 ftANSWER

7.1

The Pythagorean Theorem is only true for what type of triangle?

4.

right triangleANSWER

Guided Practice

7.1Example 3

SOLUTION

Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters.

STEP 1 Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown.

7.1 Use the Pythagorean Theorem to find the height of the triangle.STEP 2

Pythagorean TheoremSubstitute.

Multiply.Subtract 25 from each side.

Find the positive square root.

c2 = a2 + b2

12 = h

132 = 52 + h2

169 = 25 + h2

144 = h2

Find the area.STEP 3

= (10) (12) = 60 m212

The area of the triangle is 60 square meters.

Area = 12

(base) (height)

Example 3

7.1Guided Practice

Find the area of the triangle.

5.

ANSWER about 149.2 ft2

7.1

Find the area of the triangle.

6.

ANSWER 240 m2.

Guided Practice

7.1

7.1Example 4

SOLUTION

Find the length of the hypotenuse of the right triangle.

Method 1: Use a Pythagorean triple.

A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of this triangle: 5 2 = 10 and 12 2 = 24. So, the length of the hypotenuse is 13 2 = 26.

. ..

7.1

Method 2: Use the Pythagorean Theorem.

x2 = 102 + 242

x2 = 100 + 576

x2 = 676

x = 26

Pythagorean Theorem

Multiply.

Add.

Find the positive square root.

Example 4

7.1Guided Practice

7.

ANSWER 15 in.

Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple.

7.1

Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple.

8.

ANSWER 50 cm.

Guided Practice

7.1Exit Slip

1. Find the length of the hypotenuse of the right triangle.

ANSWER 39

7.1

2. Find the area of the isosceles triangle.

ANSWER 1080 cm2

Exit Slip

7.1

3. Find the unknown side length x. Write your answer in simplest radical form.

ANSWER 4 13

Exit Slip